Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency （IF） is very useful. But in noisy environments, it is hard to estimate the 1F of a multi-component Chirp signal accurately. Wigner distribution maxima （WDM） are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal 1F estimation named Wigner Viterbi fit （WVF）, based on Wigner-Ville distribution （WVD） and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error （MSE） by 50% when the signal to noise ration （SNR） is in the range of-15dB to -11dB. WVF is an effective and promising 1F estimation method.

Feature Extraction Techniques of Non-Stationary Signals for Fault Diagnosis in Machinery Systems

Previously, fault diagnosis of fixed or steady state mechanical failures (e.g., pumps in nuclear power plant turbines, engines or other key equipment) applied spectrum analysis (e.g., fast Fourier transform, FFT) to extract the frequency features as the basis for identifying the causes of failure types. However, mechanical equipment for increasingly instant speed variations (e.g., wind turbine transmissions or the mechanical arms used in 3C assemblies, etc.) mostly generate non-stationary signals, and the signal features must be averaged with analysis time which makes it difficult to identify the causes of failures. This study proposes a time frequency order spectrum method combining the short-time Fourier transform (STFT) and speed frequency order method to capture the order features of non-stationary signals. Such signal features do not change with speed, and are thus effective in identifying faults in mechanical components under non-stationary conditions. In this study, back propagation neural networks (BPNN) and time frequency order spectrum methods were used to verify faults diagnosis and obtained superior diagnosis results in non-stationary signals of gear-rotor systems.

Discrete Time-Frequency Signal Analysis and Processing Techniques for Non-Stationary Signals

This paper presents the methodology, properties and processing of the time-frequency techniques for non-stationary signals, which are frequently used in biomedical, communication and image processing fields. Two classes of time-frequency analysis techniques are chosen for this study. One is short-time Fourier Transform (STFT) technique from linear time-frequency analysis and the other is the Wigner-Ville Distribution (WVD) from Quadratic time-frequency analysis technique. Algorithms for both these techniques are developed and implemented on non-stationary signals for spectrum analysis. The results of this study revealed that the WVD and its classes are most suitable for time-frequency analysis.

Time-Frequency Entropy Analysis of Arc Signal in Non-Stationary Submerged Arc Welding

The use of time-frequency entropy to quantitatively assess the stability of submerged arc welding process considering the distribution features of arc energy is reported in this paper. Time-frequency entropy is employed to calculate and analyze the stationary current signals, non-stationary current and voltage signals in the submerged arc welding process. It is obtained that time-frequency entropy of arc signal can be used as arc stability judgment criteria of submerged arc welding. Experimental results are provided to confirm the effectiveness of this approach.

Non-Stationary Signal Segmentation and Separation from Joint Time-Frequency Plane

Multi-components sinusoidal engineering signals who are non-stationary signals were considered in this study since their separation and segmentations are of great interests in many engineering fields. In most cases, the segmentation of non-stationary or multi-component signals is conducted in time domain. In this paper, we explore the advantages of applying joint time-frequency (TF) distribution of the multi-component signals to identify their segments. The Spectrogram that is known as Short-Time Fourier Transform (STFT) will be used for obtaining the time-frequency kernel. Time marginal of the computed kernel is optimally used for the signal segmentation. In order to obtain the desirable segmentation, it requires first to improve time marginal of the kernel by using two-dimensional Wiener mask filter applied to the TF kernel to mitigate and suppress non-stationary noise or interference. Additionally, a proper choice of the sliding window and its overlaying has enhanced our scheme to capture the discontinuities corresponding to the boundaries of the candidate segments.

Analysis of Non-stationary Signals Based on Nonlinear Chaotic Theories

In the paper, two nonlinear parameter estimation methods based on chaotic theory, surrogate data method and Lyapunov exponents, are used to distinguish the difference of non-stationary signals. After brief introducting of the corresponding algorithms, two typical different non-stationary signals with different nonlinear constraining boundaries are taken to be compared by using the above two methods respectively. The obtained results demonstrate that the apparently similar signals are distinguished effectively in a quantitative way by applying above nonlinear chaotic analyses.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Features of energy distribution for blast vibration signals based on wavelet packet decomposition

Blast vibration analysis constitutes the foundation for studying the control of blasting vibration damage and provides the precondition of controlling blasting vibration. Based on the characteristics of short-time nonstationary random signal, the laws of energy distribution are investigated for blasting vibration signals in different blasting conditions by means of the wavelet packet analysis technique. The characteristics of wavelet transform and wavelet packet analysis are introduced. Then, blasting vibration signals of different blasting conditions are analysed by the wavelet packet analysis technique using MATLAB; energy distribution for different frequency bands is obtained. It is concluded that the energy distribution of blasting vibration signals varies with maximum decking charge,millisecond delay time and distances between explosion and the measuring point. The results show that the wavelet packet analysis method is an effective means for studying blasting seismic effect in its entirety, especially for constituting velocity-frequency criteria.

An Improved Signal Segmentation Using Moving Average and Savitzky-Golay Filter

Analysis of long-term EEG signals needs that it be segmented into pseudo stationary epochs. That work is done by regarding to statistical characteristics of a signal such as amplitude and frequency. Time series measured in real world is frequently non-stationary and to extract important information from the measured time series it is significant to utilize a filter or smoother as a pre-processing step. In the proposed approach, the signal is initially filtered by Moving Average (MA) or Savitzky-Golay filter to attenuate its short-term variations. Then, changes of the amplitude or frequency of the signal is calculated by Modified Varri method which is an acceptable algorithm for segmenting a signal. By using synthetic and real EEG data, the proposed methods are compared with original approach (simple Modified Varri). The simulation results indicate the absolute advantage of the proposed methods.

A Recursive Method of Time-Frequency Analysis for the Signal Processing of Flutter Test with Progression Variable Speed

Focused on the non-statlonarity and real-time analysis of signal in flutter test with progression variable speed （FTPVS）, a new method of recursive time-frequency analysis is presented. The time-varying system is tracked on-line by building a time-varying parameter model, and then the relevant parameter spectrum can be obtained. The feasibility and advantages of the method are examined by digital simulation. The results of FTPVS at low-speed wind-tunnel promise the engineering application perspective of the method.

An algorithm for frequency estimation of signals composed of multiple single-tones

The high-accuracy, wide-range frequency estimation algorithm for multi-component signals presented in this paper, is based on a numerical differentiation and central Lagrange interpolation. With the sample sequences, which need at most 7 points and are sampled at a sample frequency of 25600 Hz, and computation sequences, using employed a formulation proposed in this paper, the frequencies of each component of the signal are all estimated at an accuracy of 0.001% over 1 Hz to 800 kHz with the amplitudes of each component of the signal varying from 1 V to 200 V and the phase angle of each component of the signal varying from 0° to 360°. The proposed algorithm needs at most a half cycle for the frequencies of each component of the signal under noisy or non-noisy conditions. A testing example is given to illustrate the proposed algorithm in Matlab environment.

On-Line Structural Breaks Estimation for Non-stationary Time Series Models

Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.

Union Resolution Performance of Frequency Modulation Parameter Based on RWT for LFM Signals

Union resolution performance of FM (frequency modulation) parameter based on Radon-Wigner transform (RWT) for multi-component LFM (linear frequency modulation) signals is studied. Firstly, the RWT output expression is offered, and the independent resolution performances of initial frequency and chirp rate are analyzed. Secondly, the RWT output approximate analytic expression is given based on quadratic Taylor's series expansion, and the contour property is analyzed. Contour can be used to picture the union resolution performance of FM parameter, and 2-D resolution performance is studied based on approximate analytic expression, and the union resolution expression of FM parameter and resolution ellipse are offered. The simulation results validate the union resolution expression, and show that the union resolution can improve the resolution performance of multi-component LFM signals, contrasted with absolute resolution performance. The paper can help the study of LFM parameter estimation and resolution performance.

Dual-assisted high-precision tracking technique for wideband multiplexed signals in new generation GNSS

With the evolution of Global Navigation Satellite System(GNSS),new generation GNSS signals have adopted the dual-frequency multiplexing modulation techniques,which jointly modulate multiple signals located on multiple sub-frequencies into a Wideband Multiplexed Signal(WMS).Although WMSs were proposed initially to reduce the complexity of satellite transmitters and improve the transmission efficiency of signals,their multi-component structures and wide root mean square bandwidths introduced by high-frequency subcarriers also provide the possibility to improve the GNSS ranging precision.Therefore,this paper proposes a Dual-assisted Multi-component Tracking(DMT)technique,which can not only fully use high-frequency subcarriers in WMSs,but also effectively track carrier,subcarrier,and code by jointly utilizing all components in WMS.In this paper,the tracking and ranging performances of DMT are comprehensively analyzed theoretically and by simulation and real experiments.The results show that compared with existing WMS tracking methods,DMT can achieve tracking results with lower tracking jitters and ranging results with higher precision,providing a highly advantageous solution for new generation GNSS signal processing.

A Hybrid Time Frequency Response and Fuzzy Decision Tree for Non-stationary Signal Analysis and Pattern Recognition

A Fourier kernel based time-frequency transform is a proven candidate for non-stationary signal analysis and pattern recognition because of its ability to predict time localized spectrum and global phase reference characteristics.However,it suffers from heavy computational overhead and large execution time.The paper,therefore,uses a novel fast discrete sparse S-transform(SST)suitable for extracting time frequency response to monitor non-stationary signal parameters,which can be ultimately used for disturbance detection,and their pattern classification.From the sparse S-transform matrix,some relevant features have been extracted which are used to distinguish among different non-stationary signals by a fuzzy decision tree based classifier.This algorithm is robust under noisy conditions.Various power quality as well as chirp signals have been simulated and tested with the proposed technique in noisy conditions as well.Some real time mechanical faulty signals have been collected to demonstrate the efficiency of the proposed algorithm.All the simulation results imply that the proposed technique is very much efficient.

Applications of Fractional Lower Order Time-frequency Representation to Machine Bearing Fault Diagnosis

The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by SaS distribution model because of the presence of impulses.Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order(FLO) time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform(FLO-STFT), fractional lower order Wigner-Ville distributions(FLO-WVDs), fractional lower order Cohen class time-frequency distributions(FLO-CDs), fractional lower order adaptive kernel time-frequency distributions(FLO-AKDs) and adaptive fractional lower order time-frequency auto-regressive moving average(FLO-TFARMA) model time-frequency representation method.The methods and the exiting methods based on second order statistics in SaS distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized.Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.

Influence of maximum decking charge on intensity of blasting vibration

Based on the character of short-time non-stationary random signal, the relationship between the maximum decking charge and energy distribution of blasting vibration signals was investigated by means of the wavelet packet method. Firstly, the characteristics of wavelet transform and wavelet packet analysis were described. Secondly, the blasting vibration signals were analyzed by wavelet packet based on software MATLAB, and the change of energy distribution curve at different frequency bands were obtained. Finally, the law of energy distribution of blasting vibration signals changing with the maximum decking charge was analyzed. The results show that with the increase of decking charge, the ratio of the energy of high frequency to total energy decreases, the dominant frequency hands of blasting vibration signals tend towards low frequency and hlasting vibration does not depend on the maximum decking charge.

A Method for Gear Fault Diagnosis Based on the Empirical Mode Decomposition

According to the characteristics of gear fault vibration signals, a methodfor gear fault diagnosis based upon the empirical mode decomposition (EMD) is proposed in thispaper. By using EMD, any complicated signal can be decomposed into a finite and often small numberof intrinsic mode functions (IMFs) , which are based upon the local characteristic time scale of thesignal. Thus, EMD is perfectly suitable for non-stationary signal processing and faultcharacteristics extracting. It is well known that a gear vibration signal consists of a number offrequency family components, each of which is a modulated signal. Thus, we can use EMD to decomposea gear fault vibration signal into a number of IMF components, some of which correspond to thefrequency families, and the others are noises. Therefore, the frequency families can be separatedand the noise can be decreased at the same time. The proposed method has been applied to gear faultdiagnosis. The results show that both the sensitivity and the reliability of this method aresatisfactory.

Simulation Study on Multi-Rate Time-Frequency Analysis of Non-Stationary Signals

A new time-frequency analysis method is proposed in this study using a multi-rate signal decomposition technique for the analysis of non-stationary signals. The method uses a multi-rate filter bank for an improved non-stationary signal decomposition treatment, and uses the Wigner-Ville distribution(WVD) analysis for signal reconstruction. The method presented in this study can effectively resolves the time and frequency resolution issue for non-stationary signal analysis and the cross-term issue typically encountered in time-frequency analysis.The feasibility and accuracy of the proposed method are evaluated and verified in a numerical simulation.

IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.